Abstract
A necessary, but not sufficient, mathematical condition for the coexistence of short replicating species is presented here. The mathematical condition is obtained for a prebiotic environment, simulated as a fed-batch reactor, which combines monomer recycling, variable reaction order and a fixed monomer inlet flow with two replicator types and two monomer types. An extensive exploration of the parameter space in the model validates the robustness and efficiency of the mathematical condition, with nearly 1.7% of parameter sets meeting the condition and half of those exhibiting sustained coexistence. The results show that it is possible to generate a condition of coexistence, where two replicators sustain a linear growth simultaneously for a wide variety of chemistries, under an appropriate environment. The presence of multiple monomer types is critical to sustaining the coexistence of multiple replicator types.
Highlights
Many models of early life demonstrate competition among chemical species, which leads to processes of natural selection and, eventually, to a decrease in the chemical diversity [1,2]
The mathematical model of a prebiotic system includes the molar concentrations of two types of chemical species: n replicator units, (xi, i = 1, . . . , n), which grow in an autocatalytic manner, and λ monomers, which serve as building materials for the replicators
I error for a particular parameter set is about 48%. These results indicate a key feature for the system of algebraic equations, since 0.9% of the entire parameter space leads to the coexistence of the replicators, and the system of algebraic equations is excluding most of the possible parameter combinations that can be evaluated for coexistence
Summary
Many models of early life demonstrate competition among chemical species, which leads to processes of natural selection and, eventually, to a decrease in the chemical diversity [1,2]. Life 2013, 3 on the balance between natural selection via replication efficiency and the possibility of a sustained diversity of the chemical inventory. In this context, a space of chemical and environmental parameters is defined, where different types of autocatalytic replicators can coexist simultaneously over long periods of time. In the absence of such enzymes, a possible prebiotic scenario is that of non-enzymatic replication of alternative chemistries with less stable backbones [9,10,11,12] In this case, replicator degradation would be higher, so recycling would be even more important. The equations to describe the molar concentrations of these species are: dxi
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